Random Sets as Ill-Perceived Random Variables

The modern theory of random sets was initiated in the seventies, independently by Kendall [30] and Matheron [37] and it has been fruitfully applied in different fields such as economy, stochastic geometry and ill-observed random objects. Roughly speaking, a random set is a random element in a family of subsets of a certain universe. In particular, we can compute the probabilities that a random set hits a given set, or is included in this set, or yet includes it. In parallel and quite independently of this literature, random sets appear (but for the name) in the late sixties in the pioneering works of Dempster [16], who considers multimappings from a probability space to another space of interest.